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Former NFL Commissioner Paul Tagliabue plans to complete all hearings in the NFL's bounty probe of the Saints by Dec. 4 and make a ruling shortly after.

Such timing potentially could be disruptive for the Saints, who could lose starting defensive end Will Smith and linebacker Jonathan Vilma while trying to claw back into playoff contention.

In a document obtained Wednesday by The Associated Press, Tagliabue directs the NFL to produce key witnesses in the New Orleans Saints' cash-for-hits program, including former defensive coordinator Gregg Williams and former defensive assistant Mike Cerullo.

Four players initially were suspended, but those punishments were vacated. Commissioner Roger Goodell re-issued the suspensions with some modifications, and when the players appealed again, Goodell appointed Tagliabue to oversee the new hearings. Vilma and Smith are still playing pending the outcomes of their appeals.

Smith said he was pleased with Tagliabue's decision to hold the NFL responsible for producing witnesses who helped with the league's investigation.

"The most important thing is that Gregg Williams and those other guys are going to have to testify and be cross-examined," Smith said. "We'll see if their story stays the same."

Even as Tagliabue moves the process forward, a federal judge is still considering arguments by players that Tagliabue should be removed as arbitrator because he is biased in favor of the NFL. Based on the schedule laid out by Tagliabue, U.S. District Judge Ginger Berrigan could choose to rule as early as next week.

Smith said he was "not concerned" about the NFL's timeline calling for a decision before the season ends, adding, "Whatever happens, happens. I don't think I'll be surprised."

Vilma was not in the Saints' locker room while it was open to reporters.

They are scheduled to appear in a series of hearings in Washington D.C. running from Tuesday through Dec. 4. That means Vilma and Smith likely will be available at least for the Saints' next two games against San Francisco this Sunday and at Atlanta on Nov. 29. They could also play at the New York Giants on Dec. 9.

Vitt said after Wednesday's practice that he did not know anything about Tagliabue's schedule and declined comment, saying he's focused on getting ready for the 49ers.

Saints linebacker Curtis Lofton said the Saints cannot afford to be distracted by the possibility that they will lose Vilma and Smith late in the season, but he did not diminish the importance of the two players to the Saints' defense.

"These guys have been here for years and they're kind of like the foundation of this team," Lofton said. "So having those guys being able to play has mentally and physically been a boost to this defense and it's great to have those guys out there."

None of the players have served a game of their suspensions yet, though Vilma was barred from attending Saints training camp before Goodell's initial rulings were vacated during Week 1 of the regular season.

Vilma initially was suspended the entire 2012 season and Smith for four games.

The two other players punished are former Saints: Cleveland linebacker Scott Fujita, who is now on injured reserve, and free-agent defensive lineman Anthony Hargrove. Hargrove initially was suspended eight games, but that later was reduced to seven with credit given for the first five games he missed as a free agent. Fujita initially was suspended three games and that was later reduced to one game.

Facing resistance from the NFL Players Association and lawyers separately representing Vilma, who had argued that Goodell could not be objective, the commissioner removed himself as arbitrator in the bounty matter and appointed Tagliabue, his predecessor, in his place on Oct. 19.

Tagliabue noted in his most recent memo that other witnesses could be scheduled. Tagliabue also said he expects to decide by Monday whether to allow the Saints' personnel file on Cerullo to be included as evidence.

Players have argued that Cerullo was the NFL's primary source of information about the Saints' performance pool. They've also argued that Cerullo's credibility is in question because he was fired by the club after the 2009-10 season and he had accused the club of preventing him from getting a job on another NFL coaching staff.

The NFL investigation concluded that Saints players were rewarded for hits that knocked targeted opposing players out of games from 2009-2011. The league said there was evidence that the Saints placed bounties on star quarterbacks including Brett Favre, Kurt Warner and Aaron Rodgers.

Saints players and coaches have acknowledged they had a pool that paid rewards for big plays including interceptions, forced fumbles, sacks and big hits, similar to programs other teams have had across the league for generations. However, they say no one ever intended to injure an opposing player.